Complex number question

Hey,

I'm new as you can probably tell, so hello everyone! I'm doing AS Further Mathematics as an extra AS level during my second year at college, and I am finding it difficult to answer the following question in my homework:

Find the complex number which satisfies .

How would I go about attempting this? I'm unsure of what step/s to take first.

Let z= x+ iy. Then your equation is (2+i)(x+ iy)+(3-2i)(x- iy)=32. Multiplying that out, 2x- y+ i(x+ 2y)+ 3x- 2y+ i(-2x- 3y)= 32. Set the real part of the left side equal to 32 and the imaginary part equal to 0. You will have two equations to solve for x and y.